Trigonometry C

measurementandspace path stn adv

Trigonometry C (Path) | NSW Curriculum Website

• MA5-TRG-P-01 applies Pythagoras’ theorem and trigonometry to solve 3-dimensional problems and applies the sine, cosine and area rules to solve 2-dimensional problems, including bearings

📖 Prior Knowledge

Content	Prerequisite relationships
Right-angled Triangles	- Solve problems with Pythagoras’ theorem → Apply Pythagoras’ theorem in 3D
Trigonometry A	- Find an unknown side using trigonometry → Apply the sine rule - Find an unknown side using trigonometry → Apply the cosine rule - Find an unknown side using trigonometry → Apply the area rule for triangles - Find an unknown angle using trigonometry → Apply the sine rule - Find an unknown angle using trigonometry → Apply the cosine rule - Solve practical trigonometry problems → Apply trigonometry in 3D
Trigonometry B	- Solve elevation and depression problems → Apply trigonometry in 3D
Area and Surface Area B	- Identify slant and perpendicular heights → Interpret three-dimensional contexts

Solve 3-dimensional problems involving right-angled triangles.pdf

• Apply Pythagoras’ theorem to solve problems involving the lengths of the edges and diagonals of rectangular prisms and other 3-dimensional objects
• Apply trigonometry to solve problems involving right-angled triangles in 3 dimensions, including using bearings and angles of elevation and depression

Apply the sine, cosine and area rules to any triangle and solve related problems.pdf

• Use graphing applications to verify the sine rule $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ and that the ratios of a side to the sine of the opposite angle is a constant
• Apply the sine rule in a given triangle $ABC$ to find the value of an unknown side
• Apply the sine rule in a given triangle $ABC$ to find the value of an unknown angle (ambiguous case excluded): $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
• Use graphing applications to verify the cosine rule $c^2=a^2+b^2-2ab\cos C$
• Apply the cosine rule to find the unknown sides for a given triangle $ABC$
• Rearrange the formula to deduce that $\cos C=\frac{a^2+b^2-c^2}{2ab}$ and use this to find an unknown angle
• Use graphing applications to verify the area rule $A=\frac{1}{2}ab\sin C$.
• Apply the formula $A=\frac{1}{2}ab\sin C$, where $a$ and $b$ are the sides that form angle $C$ to find the area of a given triangle $ABC$
• Solve problems involving finding unknown angles or sides in triangles (excluding right-angled triangles) by selecting and applying the appropriate rule